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The paper deals with the state estimation of nonlinear stochastic dynamic systems with special attention on a grid-based numerical solution to the Bayesian recursive relations, the point-mass filter (PMF).
In the paper, a novel functional decomposition of the transient density describing the system dynamics is proposed.
The decomposition is based on a non-negative matrix factorization and separates the density into functions of the future and current states.

The focus of this paper is the estimation of a delay between two signals. Such a problem is common in signal processing and particularly challenging when the delay is nonstationary in nature. Our proposed solution is based on an allpass filter framework comprising of two elements: a time delay is equivalent to all-pass filtering and an all-pass filter can be represented in terms of a ratio of a finite impulse response (FIR) filter and its time reversal.

We studied the problem of sparse subspace tracking in the high-dimensional regime where the dimension is comparable to or much larger than the sample size. Leveraging power iteration and thresholding methods, a new provable algorithm called OPIT was derived for tracking the sparse principal subspace of data streams over time. We also presented a theoretical result on its convergence to verify its consistency in high dimensions. Several experiments were carried out on both synthetic and real data to demonstrate the effectiveness of OPIT.

In this paper we propose a novel and robust optimization scheme allowing to obtain the Karhunen-Lo`eve transform up to the permutation of row vectors. The introduced scheme is designed to be used in connection with artificial neural networks trained with the aid of gradient optimization techniques, and it involves two optimization criteria: (i) minimization of the mean squared error of signal reconstruction, (ii) minimization of the entropy related criterion.

A novel algorithm for designing optimized orthonormal transform-matrix codebooks for adaptive transform coding of a non-stationary vector process is proposed. This algorithm relies on a block-wise stationary model of a non-stationary process and finds a codebook of transform-matrices by minimizing the end-to-end mean square error of transform coding averaged over the distribution of stationary blocks of vectors.

Spatiotemporal regularized Discriminative Correlation Filters (DCF) have been proposed recently for visual tracking, achieving state-of-the-art performance. However, the tracking performance of the online learning model used in this kind methods is highly dependent on the quality of the appearance feature of the target, and the target feature appearance could be heavily deformed due to the occlusion by other objects or the variations in their dynamic self-appearance. In this paper, we propose a new approach to mitigate these two kinds of appearance deformation.

We propose a novel problem formulation for sparsity-aware adaptive filtering based on the nonconvex minimax concave (MC) penalty, aiming to obtain a sparse solution with small estimation bias. We present two algorithms: the first algorithm uses a single firm-shrinkage operation, while the second one uses double soft-shrinkage operations. The twin soft-shrinkage operations compensate each other, promoting sparsity while avoiding a serious increase of biases. The whole cost function is convex in certain parameter settings, while the instantaneous cost function is always nonconvex.